Questions -
Q1. A sample of thirty users of a popular social networking site yielded the histogram on the right for the number of friends. Which measure of central tendency better describes the "center of the distribution?
Choose the correct answer below.
A. The median is a better of measure of the center of the data since the distribution is skewed to the right.
B. The median is a better of measure of the center of the data since the distribution is skewed to the left.
C. The mean is a better of measure of the center of the data since the distribution is skewed to the right.
D. The mean is a better of measure of the center of the data since the distribution is skewed to the left.
Q2. Suppose a daily high temperature for a city is accidentally recorded as 700 instead of 70 degrees Fahrenheit. How would this affect the weekly mean high temperature compared to the monthly mean high temperature? Explain. Choose the correct answer below.
A. The monthly mean will be more affected than the weekly mean since there are more observations to average.
B. The monthly mean will be more affected than the weekly mean since the larger number of observations increases the impact of that individual data value.
C. The monthly mean will be less affected than the weekly mean since there are fewer observations to average.
D. The monthly mean will be less affected than the weekly mean since the larger number of observations lessens the impact of that individual data value.
Q3. The histogram shows the ages of 25 CEOs listed on a certain website. Based on the distribution, what is the approximate mean age of the CEOs in this data set? Write a sentence in context (using words in the question) interpreting the estimated mean.
Choose the correct answer below.
A. The typical CEO is between 52 and 56.
B. The typical CEO is between 60 and 64.
C. The typical CEO is between 56 and 60.
D. The typical CEO is between 64 and 68.
Q4. For each of the following, state whether a one-proportion z-test or a two-proportion z-test would be appropriate, and name the populations.
a. A student watches a random sample of men and women leaving a supermarket with carts to see whether the proportion of men who put the carts back in the designated area is greater than the proportion of women who do so.
b. The pass rate for a state's bar exam is 65%. A random sample of graduates from a law school in that state is examined to see whether their pass rate is significantly higher than 65%.
Q5. A poll organization frequently conducts polls asking the question ''In general, do you feel that the laws covering the sale of firearms should be made more strict, less strict, or kept as they are now?" At one point in time, 56% of those surveyed said "more strict." Shortly after a gun-related tragedy, 60% of those surveyed said "more strict." Use this information to complete parts a through d below.
a. Assume that both polls used samples of 590 people. Determine the number of people in the sample that said more strict" in the first survey and in the second survey. There were people who said ''more strict" in the first survey.
Q6. When comparing two sample proportions with a two-tailed alternative hypothesis, all other factors being equal, will you get a smaller p-value if the sample proportions are close together or if they are far apart? Explain.
Fill in the blanks in the sentences below.
You will get a smaller p-value if the sample proportions are ______. Assuming the standard errors are the same, the ______ the two proportions are, the ________ the absolute value of the numerator of z, and therefore the _____ the absolute value of z and the smaller the p-value.
Q7. A vaccine to prevent a severe virus was given to children within the first year of life as part of a drug study. The study reported that of the 3469 children randomly assigned the vaccine, 58 gut the virus. Of the 1598 children randomly assigned the placebo, 41 got the virus.
a. Find the sample percentage of children who caught the virus in each group. Is the sample percentage lower for the vaccine group, as investigators hoped?
b. Determine whether the vaccine is effective in reducing the chance of catching the virus, using a significance level of 0.10. The first few steps of the hypothesis-testing procedure are given. Complete the procedure.
Q8. A manufacturer withdrew Drug V from the market after a study revealed that its use was associated with an increase in the risk of heart attack. The experiment was placebo-controlled, randomized, and double-blind. Out of 1289 people taking Drug V there were 42 heart attacks, and out of 1266 people taking the placebo, there were 23 heart attacks. Perform a hypothesis test to test whether those who take Drug V have a greater rate of heart attack than those who take a placebo. Use a level of significance of 0.10. Can we conclude that Drug V causes an increased risk of heart attack?
Determine the hypotheses for this test. Let p1 represent the population proportion of heart attacks for those who take Drug V and let p2 represent the population proportion of heart attacks for those who take the placebo. Choose the correct answer below.
A. H0: P1 < P2
Ha: P1 = P2
B. H0: P1 = P2
Ha: P1 > P2
C. H0: P1 ≠ P2
Ha: P1 = P2
D. H0: P1 = P2
Ha: P1 ≠ P2
E. H0: P1 = P2
Ha: P1 < P2
F. H0: P1 > P2
Ha: P1 = P2
Q9. Some experts believe that 15% of all freshwater fish in a country have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 150 fish tested, and 24 of them have dangerous levels of mercury. Test the hypothesis that this sample is not from a population with 15% dangerous fish, assuming that this is a random sample. Use a significance level of 0.05. Comment on your conclusion.
State the null and alternative hypotheses.
A. H0: p ≠ 0.15
Ha: p = 0.15
B. H0: p = 0.15
Ha: p ≠ 0.15
C. H0: p < 0.15
Ha: p > 0.15
D. H0: p > 0.15
Ha: p < 0.15
E. H0: p = 0.15
Ha: p > 0.15
Q10. In a poll of 500 adults in July 2010, 255 of those polled said that schools should ban sugary snacks and soft drinks. Complete parts a and b below.
a. Do a majority of adults (more than 50%) support a ban on sugary snacks and soft drinks? Perform a hypothesis test using a significance level of 0.05.
State the null and alternative hypotheses. Note that p is defined as the population proportion of people who believe that schools should ban sugary foods.
A. H0: p = 0.50
Ha: p ≠ 0.50
B. H0: p = 0.50
Ha: p > 0.50
C. H0: p < 0.50
Ha: p > 0.50
D. H0: p = 0.50
Ha: p > 0.50
Q11. A true/false test has 100 questions. Suppose a passing grade is 60 or more correct answers. Test the claim that a student knows more than half of the answers and is not just guessing. Assume the student gets 60 answers correct out of 100. Use a significance level of 0.05. Steps 1 and 2 of a hypothesis test procedure are given below. Show step 3, finding the test statistic and the p-value and step 4, interpreting the results.
Step 1: H0: p = 0.50
Ha: p > 0.50
Step 2: Choose the one-proportion z-test. Sample size is large enough, because np0 is 100(0.5) = 50 and n(1- p0) = 100(.5) = 50, and both are more than 10. Assume the sample is random.
Q12. Historically, the percentage of residents of a certain country who support stricter gun control laws has been 54%. A recent poll of 1045 people showed 518 in favor of stricter gun control laws. Assume the poll was given to a random sample of people. Test the claim that the proportion of those favoring stricter gun control has changed. Perform a hypothesis test, using a significance level of 0.05.
State the null and alternative hypotheses.
A. H0: The population proportion that supports stricter gun control is 0.54, p = 0.54.
Ha: p ≠ 0.54
B. H0: The population proportion that supports stricter gun control is greater than 0.54, p > 0.54.
Ha: p < 0.54
C. H0: The population proportion that supports stricter gun control is not 0.54, p ≠ 0.54.
Ha: p = 0.54
D. H0: The population proportion that supports stricter gun control is less than 0.54, p < 0.54.
Ha: p > 0.54
E. H0: The population proportion that supports stricter gun control is 0.54, p = 0.54.
Ha: p > 0.54
Q13. In the mid-1800s, a doctor decided to make the doctors wash their hands with a strong disinfectant between patients at a clinic with a death rate of 10.4%. The doctor wanted to test the hypothesis that the death rate would go down after the new hand-washing procedure was used. What null and alternative hypotheses should he have used? Explain, using both words and symbols. Explain the meaning of any symbols you use.
State the null and alternative hypotheses using words.
A. H0: The death rate has remained the same at 10.4% after starting hand-washing.
Ha: The death rate has increased to a value greater than 10.4%.
B. H0: The death rate has remained the same at 10.4% after starting hand-washing.
Ha: The death rate has decreased to a value less than 10.4%.
C. H0: The death rate has increased to a value greater than 10.4% after starting-hand washing.
Ha: The death rate has decreased to a value less than 10.4%.
D. H0: The death rate has remained the same at 10.4% after starting hand-washing.
Ha: The death rate has changed from 10.4%.
Q14. A researcher carried out a hypothesis test using a two-tailed alternative hypothesis. Which of the following z-scores is associated with the smallest p-value? Explain.
i. z = - 0.34
ii. z = 1.56
iii. z= 2.33
iv. z= - 3.28
Which z-score has the smallest p-value?
A. z = - 3.28
B. z = 2.33
C. z = -0.34
D. z = 1.56
Q15. For each graph, indicate whether the shaded area could represent a p-value. Explain why or why not. If yes, state whether the area could represent the p-value for a one-tailed or a two-tailed alternative hypothesis.
Choose the correct answer below.
A. The shaded area could not be a p-value because it includes both tail areas.
B. The shaded area could not be a p-value because it does not include tail areas.
C. The shaded area could be a p-value for a test with a two-tailed alternative hypothesis since both tails are of equal size.
D. The shaded area could be a p-value for a test with a one-tailed alternative hypothesis because it includes tail areas.
Q16. The mother of a teenager has heard a claim that 26% of teenagers who drive and use a cell phone reported texting while driving. She thinks that this rate is too high and wants to test the hypothesis that fewer than 26% of these drivers have texted while driving. Her alternative hypothesis is that the percentage of teenagers who have texted when driving is less than 26%.
H0: p = 0.26
Ha: p < 0.26
She polls 40 randomly selected teenagers, and 5 of them report having texted while driving, a proportion of 0.125. The p-value is 0.026. Explain the meaning of the p-value in the context of this question.
Q17. Judging on the basis of experience, a politician claims that 45% of voters in a certain area have voted for an independent candidate in past elections. Suppose you surveyed 20 randomly selected people in that area, and 15 of them reported having voted for an independent candidate. The null hypothesis is that the overall proportion of voters in the area that have voted for an independent candidate is 45%. What value of the test statistic should you report?
Q18. A new drug is being tested to see whether it can reduce the chance of an asthma attack in people who have had an asthma attack in the last week. The rate of asthma attack in the population of concern is 0.19. The null hypothesis is that p (the population proportion using the new drug that have an asthma attack) is 0.19. What is the correct alternative hypothesis?
Choose the correct answer below.
A. p ≠ 0.19
B. p < 0.19
C. p > 0.19
Q19. A researcher is testing someone who claims to have ESP by having that person predict whether a coin will come up heads or tails. The null hypothesis is that the person is guessing and does not have ESP, and the population proportion of success is 0.50. The researcher tests the claim with a hypothesis test, using a significance level of 0.05. Fill in the blanks below with an accurate statement about the potential conclusion of this test.
Q20. A friend claims she can predict the suit of a card drawn from a special deck of 88 cards. There are four suits and equal numbers of cards in each suit. The parameter, p, is the probability of success, and the null hypothesis is that the friend is just guessing.
a. What is the correct null hypothesis?
A. p = ¼
B. p > 1/22
C. p = 1/22
D. p > ¼
b. What hypothesis best fits the friend's claim? (This is the alternative hypothesis.)
Attachment:- Assignment File.rar